What I'm trying to achieve is to get the following effect for a body of text:

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I've looked at many examples that use all sort of brackets, but none of them look like the ones above. So far, I've only managed to get a simple frame using mdframed, but that's far from what I hope to get.

@m0squito I added another option to my answer, this time using mdframed. Both options will admit page breaks, but the behaviour of the frame when it spans several pages is different as I set the environments; one can easily modify either of the examples to get the same resul as with the other.
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Gonzalo MedinaFeb 5 '14 at 4:19

Here I make \specbox a macro, rather than an environment, which means that the bracketed text cannot break across a page. One uses \fboxsep and \fboxrule to define the bracket offset and thickness, and \bracketarm to define the length of the bracket arm.